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Error correction iterative method for the stationary incompressible MHD flow
Author(s) -
Yang YunBo,
Jiang YaoLin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5958
Subject(s) - mathematics , magnetohydrodynamics , linearization , rate of convergence , uniqueness , convergence (economics) , iterative method , nonlinear system , compressibility , finite element method , stability (learning theory) , incompressible flow , flow (mathematics) , mathematical analysis , mathematical optimization , computer science , geometry , physics , mechanics , magnetic field , quantum mechanics , computer network , channel (broadcasting) , machine learning , economics , thermodynamics , economic growth
A new iterative finite element method for solving the stationary incompressible magnetohydrodynamics (MHD) equations is derived in this paper. The method consists of two steps at each iteration step, we need first to solve the MHD equations by the Oseen‐type iterative scheme, and then an error correction strategy is applied to control the error arising from the linearization of the nonlinear MHD equations. The new method not only maintains the advantage of the standard Oseen‐type scheme but also possesses a rapid rate of convergence. It is proved that the convergence rate of the proposed method is increased greatly under the uniqueness condition. The uniform stability and convergence of the new scheme are analyzed. Ample numerical experiments are performed to validate the accuracy and the efficiency of the new numerical scheme.